Vacancy-Assisted Diffusion in a Honeycomb Lattice and in a Diamond Lattice

Vacancy-assisted diffusion in a crystalline solid can be modeled by means of many particles jumping stochastically to their respective nearest-neighbor lattice-sites with double occupancy forbidden. The diffusion coefficient of a tagged particle, defined in terms of its mean square displacement, depends not only on the transition rate but also on the particle concentration. Nakazato and Kitahara [Prog. Theor. Phys. 64 (1980) 2261] devised a projection operator method to calculate its approximate expression interpolating between the low- and high-concentration limits for a square lattice in any dimension. In this paper, we apply their method to a honeycomb lattice and a diamond lattice, in each of which a set of the nearest-neighbor vectors depends on a site from which they originate. Compared with simulation results, our explicit expression is found to give a good interpolation in each lattice unless the host particles migrate more slowly than the tagged particle.